In linear signal processing messages transmitted over a channel are often encoded by a transmitter. At a receiver, only the encoded signal and not the complete original signal is typically received. The information contained in the original signal can be extracted, however, from the encoded signal. In particular, if the original signal can be projected onto a space that confines the signal's energy towards a certain region, then the sender only needs to transmit the non-zero components of the projected signal to allow for its full reconstruction at the receiver side. For instance, a baseband signal with a cut-off frequency fc has its energy confined in the region [−fc, fc] when projected onto the Fourier space and, as a result, a receiver can fully reconstruct the original signal without the need to observe any frequency fin the region |f|>fc. In the time space, this implies that the receiver only needs to observe one sample for every 1/fn seconds of signal, where fn=2×fc is known as the Nyquist rate.
In some situations, degradation can occur during the extraction of information from an encoded signal. Such an encoding is usually called a lossy compression. Lossy compression, in general, is concerned with the problem of finding n optimal encodings s1, s2, . . . , sn of a signal s that are transmitted over n different channels with capacities c1, c2, . . . , cn, where encoding si is transmitted over channel i and the capacities of the channels are in increasing order, ci<cj for all i<j. Generally, the optimal encoding is one in which the regions of the projected signal with higher energy are prioritized over those with lower energy. As a channel's capacity decreases, the sender stops transmitting those components that carry less energy. This implies a degradation of the received signal's quality, but in a way that such degradation is minimized.
Many known information processing systems, also known as parsers, that can extract information from structured data (also called a dataset), however, do not extract useful information from only a portion of the dataset. Instead, these parsers typically analyze the complete dataset. Many conventional parsers and/or processing systems lack capacity to process large datasets including, e.g., megabytes, several hundred megabytes, gigabytes, terabytes, or even larger datasets. For example, such parsers may run out of memory and/or the maximum time allowable for processing the dataset. In some situations, while several conventional parsers and processing systems can process the datasets, they may be inefficient and may require large amounts of memory and/or storage, a large number of processors, substantial processing time (e.g., several minutes, hours, or even days), etc.
Similarly, if dataset is received at a high rate, e.g., at several Mbytes/s, Gbytes/s, etc., a conventional parser may not be able to parse the complete dataset at such a high rate. Some conventional parsers, therefore, ignore certain portions of the received dataset. The portions that are not processed by a parser are often selected at random or in a nondiscriminatory manner. The resulting extraction of information can be incomplete and/or inaccurate.